报告题目：Invariant Manifolds of Stochastic Retarded Partial Differential Equations and its approximations

报告人：赵君一郎 副教授（西南交通大学）

邀请人：李扬荣 教授

报告时间：2025年12月07日 10:00

报告地点：数统大楼学术报告厅912

参加人员：教师、研究生、本科生

报告摘要：We construct invariant manifolds for a class of stochastic retarded partial differential equations (SRPDEs) and their approximations with respect to the driving noise. For both additive and multiplicative noise cases, we use the Wiener shift to define processes providing stationary noise approximations and establish pointwise convergence of the solutions for these approximations to the original SRPDE solutions. For additive noise, we prove the existence of smooth inertial manifolds for the stationary approximations and show that these manifolds converge to those of the original SRPDE. In the multiplicative noise case, we restrict our analysis to a local random region, proving the existence of Lipschitz invariant manifolds for both the original system and its approximations, the convergence result for the manifolds is also established.

报告人简历： 赵君一郎，西南交通大学数学学院副教授，博士生导师，博士毕业于美国杨百翰大学，自博士阶段起一直从事随机微分方程和无穷维动力系统方向相关的研究工作，为西南交通大学数学学院分析与方程团队成员，已有多项研究成果发表在Journal of Differential Equations、Journal of Dynamics and Differential Equations、Proceedings of AMS等国际知名数学期刊，入选2021年度四川省天府峨眉计划青年人才项目，主持国家自然科学基金青年基金、面上项目基金各一项，参与国家级和省部级项目若干项。